NCERT Class 9 Mathematics

INTRODUCTION TO MATHEMATICAL MODELLING 309

File Name : C:\Computer Station\Maths-IX\Chapter\Appendix\Appendix–2 (03–01–2006) PM65

So, I = 1200n (1)

gives the relationship between the number of years and interest, if Rs 15000 is invested
at an annual interest rate of 8%.

We have to find the period in which the interest earned is Rs 4000.
Putting I = 4000 in (1), we have

4000 = 1200n (2)

Step 2 : Solution of the problem : Solving Equation (2), we get

n =

4000 1

3

1200 3

✁

Step 3 : Interpretation : Since n =

1

3

3

and one third of a year is 4 months,

Sudhir can buy a washing machine after 3 years and 4 months.

Can you guess the assumptions that you have to make in the example above? We
have to assume that the interest rate remains the same for the period for which we

calculate the interest. Otherwise, the formula I =

P

100

nr

will not be valid. We have also

assumed that the price of the washing machine does not increase by the time Sudhir
has gathered the money.

Example 3 : A motorboat goes upstream on a river and covers the distance between
two towns on the riverbank in six hours. It covers this distance downstream in five
hours. If the speed of the stream is 2 km/h, find the speed of the boat in still water.

Solution : Step 1 : Formulation : We know the speed of the river and the time taken
to cover the distance between two places. We have to find the speed of the boat in
still water.

Mathematical Description : Let us write x for the speed of the boat, t for the time
taken and y for the distance travelled. Then

y =tx (1)

Let d be the distance between the two places.

While going upstream, the actual speed of the boat

= speed of the boat – speed of the river,

because the boat is travelling against the flow of the river.

So, the speed of the boat upstream = (x – 2) km/h

It takes 6 hours to cover the distance between the towns upstream. So, from (1),

we get d =6(x – 2) (2)